The Territorial Cup Series is a year-long competition, based on a point system, and is between Arizona State and the University of Arizona for both men’s and women’s sports.
Each respective sport also has their Territorial Cup in a sense, like Arizona Football who took back the cup this last season.
Here is the official description and point system according to the State Farm Territorial Cup Series website (note: the site hasn’t been updated since 2012):
Each year, the schools’ athletic departments compete head-to-head in eighteen (18) common, equally weighted, sports to determine which community can claim the bragging rights for that year.